### Nuprl Lemma : p-inject_wf

`∀[A,B:Type]. ∀[f:A ⟶ (B + Top)].  (p-inject(A;B;f) ∈ ℙ)`

Proof

Definitions occuring in Statement :  p-inject: `p-inject(A;B;f)` uall: `∀[x:A]. B[x]` top: `Top` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` union: `left + right` universe: `Type`
Definitions unfolded in proof :  p-inject: `p-inject(A;B;f)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r B` uimplies: `b supposing a` so_apply: `x[s]`
Lemmas referenced :  all_wf assert_wf can-apply_wf equal_wf do-apply_wf top_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality lambdaEquality because_Cache functionEquality functionExtensionality applyEquality hypothesis independent_isectElimination axiomEquality equalityTransitivity equalitySymmetry unionEquality isect_memberEquality universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  (B  +  Top)].    (p-inject(A;B;f)  \mmember{}  \mBbbP{})

Date html generated: 2018_05_21-PM-06_32_54
Last ObjectModification: 2017_07_26-PM-04_51_55

Theory : general

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